Therefore, the spacetime geometry is changed by the tiny amount given by equation(REF ). We would like to calculate how the geometry changes. Using the linearized perturbation theory of general relativity, the Riemannian tensor is given by [1]}
\(R_{\mu \nu \rho \sigma }=\frac{1}{2}( \partial _{\rho }\partial _{\nu } h_{\mu \sigma } +\partial _{\sigma }\partial _{\mu }h_{\nu \rho }-\partial _{\sigma }\partial _{\nu }h_{\mu \rho }-\partial _{\rho }\partial _{\mu }h_{\nu \sigma } ) \,.\) 
